1. Technical Field
This invention concerns a method for stabilizing the operation of fractionally spaced equalizers used in digital signal receivers, having a plurality of equalization coefficients, said equalization coefficients being updatable through minimization of a proper cost function and stabilizable through a proper change of said cost function, said cost function entailing the use of a virtual noise matrix. The invention concerns also the relating fractionally spaced equalizer and the digital signal receiver incorporated in it.
2. Discussion of Related Art
Adaptive equalization is a technique commonly used to compensate the channel distorting effect in a general transmission system. According to a known technique synchronous equalizers obtained through FIR (Finite Impulse Response) filters are used with variable coefficients time-spaced by an amount equal to the signal interval or to the symbol time.
Improved performance may be obtained using the so called fractionally spaced equalizers (FSE) consisting of an adaptive FIR filter with coefficients time-spaced by an amount equal to a fraction of the signal interval or to the symbol time. Performances of the fractionally spaced equalizer with a sufficient number of coefficients are practically independent from the phase characteristics of the transmission channel and from the phase of the symbol synchronism as reconstructed during reception. More generally, a fractionally spaced equalizer is able to execute, in an adaptive manner, and only in one device, both the adaptive filtering and equalization functions, for instance, to emulate the optimum linear receiver.
However, the fractionally spaced equalizer has two main drawbacks: first of all, the coefficient drift phenomenon and, secondly, its low convergence rate. Both said drawbacks are due to the fact that a fractionally spaced equalizer generally has more configurations than the coefficients, which substantially correspond to the same root-mean-square error or, more generally speaking, to the same value of the cost function of the equalized signal. In other words, the cost does not significantly change according to certain directions around the point corresponding to the optimum configuration point of the coefficients.
It has been proved through experimental tests that a fractionally spaced equalizer is affected by a long term instability due to the unavoidable bias occurring in the control circuits. This behaviour leads the equalizer to operate with coefficients whose values are so high to cause `overflow` phenomena in the registers or coefficient saturation, with a consequent performance deterioration. Therefore, in order to maximize the performance of a fractionally spaced equalizer it is necessary to apply proper control algorithm stabilization techniques capable of avoiding the coefficient drift and increasing the convergence rate. To this end it has been proposed, for instance in the article by R. D. Gitlin, H. C. Meadors, S. B. Weinstein, `The Tap-Leakage Algorithm: An Algorithm for the Stable Operation of a Digitally Implemented Fractionally Spaced Equalizer`, Bell Sys. Tech. J., vol. 61, no. 8, pp. 1817-1839, October 1982, to change the control algorithm of the fractionally spaced equalizer by introducing a predetermined amount of white noise. Said technique, called `tap-leakage`, is an efficient measure against coefficient drift while improving convergence rate. Nevertheless, the performances of the fractionally spaced equalizer are worsened, since the fictitious noise outside the signal band contributes to stabilization, whereas the fictitious noise inside the band jeopardizes the achievement of an optimum coefficient configuration. Therefore, in the article `A new Tap-Adjustment Algorithm for the Fractionally Spaced Equalizer`, by T. Uyematsu e K. Sakaniwa, GLOBECOM '85, pp. 1420-1423, December 1985, suggests to introduce a fictitious noise with a non white spectral power density, i.e. not constant with the frequency change, and more specifically, a substantially non zero spectral power density only where the spectral power density of the signal is zero. This technique is mainly limited in that it does not allow a complete stabilization of the adaptive equalizer, as in the `roll-off` area of the signal, i.e. the transition area from the maximum spectral power density to zero, there are still a large number of coefficient configurations associated with the same value of the root-mean-square error.
A possible remedy to the drawbacks of the previous techniques is also suggested by G. Karam, P. Moreau, H. Sari, `Stabilizing Fractionallyly Spaced Equalizers`, GLOBECOM '91, IEEE Global Telecommunication Conference 1991, pp. 1807-1811, where a constraint is added to the technique proposed by Uyematsu and Sakaniwa on the transfer function form realized by the adaptive equalizer under steady state conditions. This approach requires for the equalizer itself to calculate its output signal at a frequency at least equal to (1+.alpha.)/T, where T is the symbol time and .alpha. the amplitude of the roll-off area. Such a calculation increases in fact the implementative complexity of the equalizer, since calculation of the signal on the equalizer output at frequency 1/T is usually enough.
Another possible remedy to the drawbacks of Gitlin, Meadors, Weinstein and Uyematsu and Sakaniwa's methods is the use of a whitening filter upstream of the equalizer and the addition of white noise (for a description of such a technique see A. Spalvieri, C. Luschi, R. Sala, F. Guglielmi, `Stabilizing the Fractionally Spaced Equalizer by Prewhitening`, GLOBECOM '95, IEEE Global Telecommunication Conference, Singapore, Nov. 1995, pp. 93-97). However, this technique disadvantageously requires addition of a whitening filter and a higher precision in the equalizer algebras.